If a solid sphere of mass M and radius R is rotating about an axis through its c

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Question: If a solid sphere of mass M and radius R is rotating about an axis through its center, what is its moment of inertia?

Options:

Correct Answer: 2/5 MR^2

Solution:

The moment of inertia of a solid sphere about an axis through its center is I = 2/5 MR^2.

If a solid sphere of mass M and radius R is rotating about an axis through its center, what is its moment of inertia?

If a solid sphere of mass M and radius R is rotating about an axis through its center, what is its moment of inertia?

Step 1: Understand what moment of inertia means. It is a measure of how difficult it is to change the rotation of an object.
Step 2: Identify the shape of the object. In this case, it is a solid sphere.
Step 3: Know the formula for the moment of inertia of a solid sphere rotating about an axis through its center. The formula is I = 2/5 MR^2.
Step 4: Recognize the variables in the formula: M is the mass of the sphere, and R is the radius of the sphere.
Step 5: Substitute the values of M and R into the formula if you have them, or use the formula as is to understand the relationship.

Moment of Inertia – The moment of inertia is a measure of an object's resistance to changes in its rotation about an axis.
Solid Sphere Properties – Understanding the geometric and physical properties of a solid sphere is essential for calculating its moment of inertia.
Axis of Rotation – The axis through which the object rotates affects the calculation of the moment of inertia.